The ALLM parameterization of sigma_{tot}(gamma* p) - an update

TL;DR

The paper presents ALLM97, an updated ALLM parameterization that describes the total gamma*-p cross section across the full Q^2 range, including Q^2=0, by fitting to all published F2 data. It demonstrates excellent agreement with a wide corpus of data (F2, F2 slopes, and sigma_tot) and achieves a chi^2/ndf of 0.97 for 1356 points. The update reveals a substantially shifted Pomeron scale and a smooth transition between soft and hard dynamics, enabling a unified description of both low and high-Q^2 regimes. This parameterization provides a practical tool for corrections and for exploring the interplay between nonperturbative and perturbative QCD.

Abstract

The ALLM parameterization of sigma_{tot}(gamma* p) has been updated by using all published F_2 data to determine its parameters. The fit yields a chi^2/ndf of 0.97 for the 1356 data points. The updated ALLM parameterization, ALLM97, gives a good description of all the available data in the whole x and Q^2 range studied so far (3\times10^{-6} < x < 0.85, 0 \le Q^2 < 5000 GeV^2).

Figures (12)

• Figure 1: The total $\gamma^* p$ cross section as function of $W^2$, for different $Q^2$ values. The curves are the expectations of the ALLM parameterization.
• Figure 2: The total $\gamma^* p$ cross section as function of $W^2$, for different $Q^2$ values. The curves are the results of the ALLM-N parameterization.
• Figure 3: The intercept of the Pomeron trajectory as function of $Q^2$, as obtained from the ALLM parameterization. The dotted line shows the uncertainty of the fit.
• Figure 4: The intercept of the Pomeron trajectory as function of $Q^2$, as obtained from the ALLM97 (full line) and ALLM91 (dotted line) parameterizations.
• Figure 5: The dependence of the proton structure function, $F_2(x,Q^2)$, on $Q^2$ for fixed $x$ values as indicated in the figure. For display purposes, the structure function values have been scaled at each $x$ by the factor shown in brackets under the $x$ values. The curves are the results of the ALLM97 parameterization.